They've described each other as "vulgar" and "wacko", they believe they can pluck voters from each other's base, they pack more supporters in their rallies than probably all the other presidential candidates combined.

They draw support from the same well of frustration but at opposite ends of the political spectrum. They're both older, white men who engage in long jeremiads about anger - yet they couldn't be more different.

Bernie Sanders is the 74-year-old self-declared socialist senator from Vermont (though he was born and raised in Brooklyn) who runs uplifting ads about people coming together around a common vision for America.

Donald Trump is the 69-year-old Queens-born billionaire business tycoon and television personality, married three times, who called for a ban on all Muslims entering the US and just threw a curveball into the race by announcing he was skipping Thursday's Republican debate.

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There is a unifying theme to the two men's campaign: anger and a sense of betrayal, although it is expressed very differently in Trump and Sanders rallies.

They are tapping into a deep frustration with the political system, which was detailed in a NBC and Wall Street journal poll in November 2015. The poll found that 69% of respondents, across all demographics and party affiliation felt "angry because our political system seems to only be working for the insiders with money and power, like those on Wall Street or in Washington, rather than working to help everyday people get ahead."

But three out of four Democrats are proud of the path their country is on, and the progress it is making as "tolerant nation." So if Mr Trump's supporters want to roll back everything that President Barack Obama has done over the last seven years, including marriage equality and healthcare reform, the frustration of Mr Sanders' fans comes from what they perceive as the slow pace of change.

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Mr Sanders would like you to know that although he is angry, he is also hopeful and believes in positive change. In December on CBS network television he described the differences between him and Mr Trump, whom he described as vulgar.

"What Trump has done with some success is taken that anger, taken those fears which are legitimate, and converted them into anger against Mexicans, anger against Muslims, and in my view that is not the way we're going to address the major problems facing our country," he said.

Mr Sanders said he could make the case to Mr Trump's "working-class and middle-class support," that to address these issues "we need policies that bring us together".

In much less eloquent language, Mr Trump tweeted that he could draw support away from Mr Sanders: "Strange, but I see wacko Bernie Sanders allies coming over to me because I'm lowering taxes, while he will double & triple them, a disaster!"

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Washington Post columnist EJ Dionne said that the "deep idealism in the Sanders (supporters) is still rooted in a belief that change can bring about good things."

"To the extent there's any idealism in Trump, it's nationalism. People on the left discount it but it's a consistent piece of the Republican repertoire. Nationalism is central to Trumpism," added Mr Dionne, author of Why the Right Went Wrong, an examination of the crescendo cycle of betrayal and disappointment experienced by Republican conservatives, which Mr Dionne traces back to the 1950's.

The other radical front-runner in the Republican race, the evangelical Texas senator Ted Cruz, is the candidate that conservatives believe truly represents them. But Trump draws the crowds.

The Republican and Democratic insurgents garner roughly the same level of support nationally on either side of the aisle. In a large field where support for any candidate is diluted, Mr Trump gets between 20 and 30% support from Republican primary voters - the same amount of support Mr Sanders gets from Democratic supporters in a field overwhelmingly dominated by Mrs Clinton.

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The Republican and Democratic left-field candidates attract thousands to their rallies, crowds most of their rivals could only dream of. Mr Trump appeals mostly to low-income voters with no university degree while Mr Sanders is hugely popular with young voters and university students.

Yet coverage of Mr Trump dominates the media. As of December last year, Mr Trump had received 234 minutes of US network news coverage, while Mr Sanders received all of 10 minutes.

The comparison is also imperfect, of course, because while Mr Trump is leading by a wide margin in national polls and in all four first states in the primary race, Mr Sanders leads only in New Hampshire, which borders Vermont. His democratic rival Hillary Clinton is at least 20 points ahead of him in national polls and is expected to clinch the nomination.

For now, it's hard to see an "establishment'' candidate emerge on the Republican side who can articulate voters' fears the way Mr Trump has done.

It is of course true that the United States is changing rapidly demographically, that there is a lack of social mobility, rising inequality and wage stagnation. America is also in relative or absolute decline on the world stage, depending on who you ask.

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And change is unsettling. The NBC/WSJ poll found that 71% of Republican primary voters "felt out of place" in their own country, due to things like illegal immigration and advancement of gay and lesbian rights. These are not sentiments that can be dismissed with a flick of the hand.

But people are also nostalgic for halcyon days that never quite existed. When Mr Trump promises to "make America great again" it is precisely this intangible yearning that he taps into.

Vin Weber, a former congressman who came to office during the Reagan administration and is now a Jeb Bush supporter, said that while the political and economic environment do make people feel like they've been betrayed, the "notion that someone is going to come in and do something overnight and change all this, whether it's expelling all immigrants or building a wall (Trump), or punishing the banks (Sanders), that's not going to solve it."

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Mr Weber ties the mood in the US to a global trend, a long-term decline in respect for institutions in the US that is mirrored with a broader decline for institutions worldwide - and a general sense of malaise.

That is where the candidates let their voters down.

"Neither one is really talking honestly to the public about the fact that the world is changing."